A requirement has arisen in recent years for high-quality reproduction of images which have varying degrees of density, i.e. exhibit gray-scale variations, in addition to reproduction of material such as characters, numerals etc. which have only two possible density values, by means of a bi-level type of display device such as a dot-matrix display which is inherently capable of generating only two levels of display density. There have been various proposals made for implementing pseudo-continuous tone reproduction by such display devices, through the use of a spatial gray scale. Such methods are based on setting a relatively high proportion of picture elements of the display in a first display state within a display region which is to represent a light (i.e. low-density) region of the original image, and a high proportion of the picture elements in a second display state in the case of a dark (i.e. high-density) region of the original image.
The most well-known method of providing such pseudo-continuous tone reproduction is a dither technique whereby a step gradation representation of a continuous tone image is reproduced on the basis of numbers of dots within each of predetermined areas of the continuous tone image, by utilizing a dither matrix. Threshold values of the dither matrix are compared with the level of an input signal, one picture element at a time, to thereby execute bi-level image conversion processing. However this method has the disadvantage that the step gradation reproduction characteristic and the resolution of the image that is obtained will both depend directly upon the size of the dither matrix, and have a mutually incompatible relationship. Moreover with the dither technique, it is difficult to avoid the generation of textures and moire patterns in the reproduced image, particularly when printed images are reproduced.
A method has been proposed in the prior art which is highly effective in overcoming these problems of the dither method. This is the "error diffusion" method, which has been proposed by R. Floyd and L. Steinberg under the title "An Adaptive Algorithm for Spatial Gray Scale", published in the SID 75 Digest, pp 36-37. With that method, an amount of error that is found between the actual density level of a picture element of an original image and the bi-level value of density that is determined for the bi-level display device (i.e. which must be either a maximum or a minimum value) is apportioned among a set of picture elements which have not yet been processed and are positioned peripherally adjacent to the picture element that is currently being processed. In this way the effects of each bi-level conversion error for a picture element is "diffused" among a plurality of adjacent picture elements, to thereby provide greater accuracy of image reproduction.
FIG. 1 is a conceptual block diagram of an embodiment of an apparatus for implementing a modified form of the above error diffusion method, having the objective of providing substantially better image reproduction than is possible with a direct implementation of the error diffusion method as proposed in the aforementioned article. The apparatus of FIG. 1 has been proposed in the aforementioned copending commonly assigned application by Maruyama et al, Ser. No. 110,082. The basic principles of this apparatus are as follows. Sequential input level values representing quantized density levels of respective picture elements of an original image (picture elements of a field of a video signal, for example), are supplied to the apparatus via an input terminal 4. An input signal level for a picture element that is currently being processed (referred to in the following as the object picture element) is designated as I.sub.xy. The picture elements of the original image correspond to a rectangular array, as illustrated in FIG. 2, and these picture elements are successively processed (i.e. with corresponding input level values being successively applied to the input terminal 4) along each line of picture elements in the x-direction as indicated in FIG. 2, with successive lines being processed in the y-direction. A set of positions of four picture elements which have not yet been processed and are disposed peripherally adjacent to the object picture element are designated as A, B, C and D respectively, these being the matrix positions (x+1, y), (x+1, y+1), (x, y+1) and (x-1, y+ 1), with the object picture element position designated as (x,y). The input level I.sub.xy is added to an accumulated error S.sub.xy for the object picture element (described hereinafter) in an adder 5, to obtain a compensated input level I'.sub.xy. This is compared with a fixed threshold value by a comparator 8, to thereby execute bi-level conversion of I'.sub.xy, to obtain a corresponding output value P.sub.xy. The degree of error of P.sub.xy with respect to I'.sub.xy is then obtained by a subtractor 9, and is referred to as a bi-level conversion error E.sub.xy. Upon completion of processing the object picture element to obtain the corresponding output value P.sub.xy, the bi-level error value E.sub.xy is multiplied by each of four specific apportionment factors, with the resultant apportioned error values being added to respective values of accumulated error which had been previously stored in the memory 1 at locations corresponding to the peripheral picture element positions A, B, C and D, to thereby obtain updated values of accumulated error. These updated values are then stored back in the memory 1 at the same locations.
It can thus be understood that the accumulated error value for the object picture element, which is stored at position 3 in the memory 1, has been obtained by successively adding four values of apportioned bi-level conversion error, respectively derived during the preceding four picture element processing steps. This accumulated error value, designated as S.sub.xy, is added to tha input level I.sub.xy in the adder 5, to obtain the aforementioned compensated input level I'.sub.xy for the object picture element. In this way, the input signal level I.sub.xy of the object picture element is compensated based upon four values of bi-level conversion error (E.sub.xy) that were respectively obtained from the subtractor 9 during processing of the picture elements at positions (x-1,y-1), (x, y-1), (x+1, y-1), and (x-1, y) in FIG. 2.
Such a prior art error diffusion method has the advantages over the aforementioned dither method of an improved density gradation characteristic, and improved resolution, together with only a very small degree of moire pattern being produced when a printed image is reproduced. However by comparison with a prior art method known as the Correlative Density Assignment of Adjacent Pixels, or CAPIX method, such a prior art error diffusion method is inferior with regard to the density gradation characteristic and resolution, and is also inferior with regard to generation of unwanted texture patterns in regions of uniform density of the reproduced image. The CAPIX method is based on a random dither technique, utilizing cumulative density reapportionment